I understand that as I increase ISO, I'll increase the amount of noise in the resulting image. With a constant aperture I can decrease ISO and slow the shutter speed (assume a non-moving subject, camera on a tripod etc, so shutter speed won't introduce any blur). My question is, will the image noise of a high ISO/fast shutter speed be the same as a low ISO/slow shutter speed where both settings provide the same total amount of exposure?

I'm looking for answers that pertain to modern DSLR's, not film, in case it makes a difference.

7 Answers
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Image noise in a properly operating DSLR will be affected by shutter speed, but not in the linear relationship the question implies. In decreasing order of impact, image noise is a factor of:
- Amplification applied to the sensor cells (higher ISO increases noise)
- Thermal noise (hotter sensor is noisier)
- Duration of exposure (longer the capture, more the cumulative random pixels lit up)

Duration related noise is also interrelated with thermal noise, since keeping the sensor powered for longer will cause more heat to be generated.

Overall, in a given shooting environment, increasing ISO has the greatest detrimental effect, going by empirical evidence from a fair bit of night photography done using a Canon 1D Mark III, Canon 5D Mark II, and a couple of non-SLRs, a Minolta DiMAGE A2 and DiMAGE A200.

Summer evening shots also seem to have greater visible noise (I see more random red dots than other colors, oddly) than cold winter evening shots.

I've seen significant noise from thermal/duration after a 30-60 minute exposure. It looks quite different to the "high ISO noise", in that it's single "hot pixels" of red, green or blue, much brighter but also much sparser than "high ISO noise"
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drfrogsplatNov 22 '12 at 1:30

Also, you can reduce the thermal/duration noise by enabling your camera's "dark frame noise reduction" (goes by various names). It basically takes a second photo immediately after, with the same duration, but without opening the shutter, and subtracts that supposedly "dark frame" from the first, which can remove those "hot pixels" and other systematic bias in the noise.
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drfrogsplatNov 22 '12 at 1:32

Lots of good information in all these answers, and yes I had in my mind that there might be a linear relationship between ISO and shutter speed.
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JeffNov 29 '12 at 17:22

Technically speaking, increasing ISO does not actually "increase noise". When you increase the ISO setting, you are actually just instructing the camera to change what level of charge represents "maximum saturation" (the point at which a pixel should reach its maximum numeric value, which in the case of a 14-bit sensor is 16384.)

The primary cause of noise in an image is the random distribution of photons as they reach the sensor. The fewer photons reaching the sensor, the more apparent their random distribution will be...thus the visible "grain". The amount of noise you see in a photo is inversely related to the amount of light reaching the sensor. Less light, more noise...more light, less noise. For a given exposure time, when you get less light down the lens, you expose fewer photons per pixel, and since photons are effectively distributed randomly, some pixels may get less than they should while others get more than they should. That uneven distribution is the specific cause of photon shot noise. When you get more light onto the sensor, the random nature of light will distribute more and more evenly across the area of the sensor, and as the average number of photons per pixel increases and normalizes, the effects of photon shot noise will lessen.

When you crank up the ISO to produce a "proper" exposure for that small amount of light, you amplify the sensor signal, which exaggerates the effect that photon shot noise has. Alternatively (assuming an ideal sensor that introduces no electronic noise of its own), you could always expose at ISO 100, then boost exposure by the necessary number of stops in post, and experience the same effect. It is not the amplification, be it analog or digital, that creates noise...it simply enhances the effects of noise.

"My question is, will the image noise of a high ISO/fast shutter speed be the same as a low ISO/slow shutter speed where both settings provide the same total amount of exposure?"

Shutter speed is something you can use to control what ISO setting you need. Shutter speed is exposure time, and if you can only get 1/4 the amount of light down the lens that you need to be able to use ISO 100, you can always expose four times as long. There are caveats to this...if you are photographing anything with motion, you'll see motion blur in the final photo if shutter speed is too slow. Slower shutter speed can also lead to blur from camera shake, which can reduce the sharpness and contrast of your photo. If you are photographing a still scene...such as a landscape or still life, you probably have the option of reducing shutter speed rather than increasing ISO to achieve a proper exposure. The longer exposure will allow more light to reach the sensor, and the use of a lower ISO will require less amplification, reducing noise on two fronts (more light/less noise, less amplification/less noise.)

So the answer to your question is NO, if you trade a high ISO/fast shutter for low ISO/slow shutter, you should end up with LESS NOISE (but potentially more motion blur or blur from camera shake if you are shooting hand-held.)

No. Noise does increase with shutter-speeds but only marginally so. The amount of noise you get from ISO amplification is much greater. You also lose a lot of dynamic-range by raising the ISO which won't happen with low shutter-speeds until truly extreme cases.

Shutter speed has no effect on noise in your images - unless you are in modes like "Shutter Priority" where other settings are automatically changed for you to keep a certain exposure. You can try this by setting your camera to full manual and switch between shutter speeds. You will just see your image get darker/lighter as your shutter speed decreases/increases.

ISO changes the sensitivity of the sensor to the incoming signal. However, this also means any noise is also amplified in the final output. So, increase ISO and you have more noise and higher effective exposure. Decrease ISO and you have less noise but lower effective exposure (assuming everything else is equal).

So if you do choose lower ISO and slower shutter speed and somehow get the same exposure (maybe you are changing the aperture or adding light to the scene), you will get less noise in your images.

I've experienced noise problems when using low ISO say below 400 ISO with high shutter speeds of over say 4000 or 6000sec and really bad from 6500 to 8000 sec. in really bright light. So I've been trying to keep ISO and shutter speed some what balanced like keeping shutter speed down to 1250 or 2000 sec with ISO 400. And higher ISO when using fast shutter speeds. I experienced this while experimenting with trying to eliminate blur from fast moving subjects while hand holding long focal length lens's.

I agree. May I add that in bright light I like to step up the iso setting (which would be set to minimum otherwise) to achieve top shutter speed, and 400 seems to be a well balanced value. To illustrate this, here two shots I've taken handheld with a very long telephoto (~300mm x2 m4/3 crop factor): flickr.com/photos/sagemess/16809353092.
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B2FApr 12 at 17:00